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research article

Long range orders in models of itinerant electrons interacting with heavy quantum fields

Macris, N  
•
Piguet, C A
2001
Journal of Statistical Physics

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on Zd, d \ 2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the ‘‘Ising spins’’ are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to p. We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed.

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Type
research article
DOI
10.1023/A:1013509512844
Web of Science ID

WOS:000172822600008

Author(s)
Macris, N  
•
Piguet, C A
Date Issued

2001

Published in
Journal of Statistical Physics
Volume

105

Issue

5/6

Start page

909

End page

935

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LTHC  
Available on Infoscience
February 16, 2007
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/3155
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